The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. Find the original number.

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Solution

The correct option is A 71
Let the two-digit number be $10 x + y$
Then, we have : $x + y = 8$ .......... (1)
and $10 y + x = 10 x + y - 54 o r, x - y = 54 / 9 = 6$ ............ (2)
Solving equations (1) and (2), we get
$x = (8 + 6) / 2 = 7$ and $y = 1$
$∴$ The required number $= 7 \times 10 + 1 = 71$

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The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. Find the original number.

The correct option is A 71Let the two-digit number be 10x+yThen, we have : x+y=8 .......... (1)and 10y+x=10x+y−54or,x−y=54/9=6 ............ (2)Solving equations (1) and (2), we getx=(8+6)/2=7 and y=1∴ The required number =7×10+1=71